Harrison and sherrie are making decisions about their bank accounts. harrison wants to deposit $200 as a principle amount, with an interest of 2% compounded quarterly. sherrie wants to deposit $200 as the principle amount, with an interest of 4% compounded monthly. explain which method results in more money after 2 years. show all work.

We first solve for the effective interest rate by dividing the nominal rate by the number of time periods in a year, adding 1, and exponentiating to that number of time periods.
The effective interest rate for Harrison is (1+0.02/4)^4 = 1.02015. After 2 years, his money will have grown to ($200)(1.02015)^2 = $208.14.
The effective interest rate for Sherrie is (1+0.04/12)^12 = 1.04074. After 2 years, her money will have grown to ($200)(1.04074)^2 = $216.63.
Therefore, Sherrie will have more money than Harrison.